Bowling balls have gripping holes and balance holes, some of which may often require relocation. The old holes are plugged or filled with epoxy resin or other plastic material. The excess filling material protrudes and must be machined down even with the spherical surface of the ball. A prior machine for this purpose is shown for example in U.S Pat. No. 3,106,133 to J. Arpanio, Jr. et al, and employs a router mounted in a bell jar. There is a need for an improved machine capable of greater precision, faster operation, and better visibility of the work.